Let n axc b100 x Solve for a Solve for b Solve for c Solv

Let n = a/x-c + b(100 - x) Solve for a. Solve for b. Solve for c Solve for x

n = a/(x-c) +b(100-x)

solve for a)

n - b/(100-x) = a/(x-c)

n(x-c) - b(x-c)/(100-x) = a

b) Solve for b:

n -a/(x-c) = b(100-x)

b = n/(100-x) - a/(x-c)(100-x)

c) Solve for c

n -b(100-x) = a/(x-c)

x-c = a/{ n -b(100 -x) }

c = x- a/{ n -b(100 -x) }

d) solve for x:

n - b(100-x) = a/(x-c)

n(x-c) - b(100-x)(x-c) = a

nx -nc -b ( 100x -100c -x^2 +xc) =a

bx^2 + x( -100b+n) +100bc = a

use the quadratice root formula :

x = [ 100b -n +/- sqrt( (n-100b)^2 - 400b^2c]/2b